The approach that we benchmarked in this study offers some flexibility on its implementation. For instance, given that QAMPA is not fully grounded on insights from a specific Hamiltonian evolution, it might be worth asking whether the information related to the coefficient of objective function (\(J_{nm}\) ) are beneficial as inserted in the circuit or if it sufficient to train the parameters using that information, like done for VQE hardware-efficient ansätze [1]}.
We investigated empirically these questions by comparing instance-by-instance results for QAOA and QAMPA, using \(\mathtt {scanlast}\)  on a set of instances for \(N=10\)  with slightly modified parameters (\(f_{opt}=200p\) ). The results are statistically in line with the ones presented for \(N=16\)  in Figure REF  using higher computational effort.
